Import mul! from LinearAlgebra in butterflylu.jl

[ChrisRackauckas-Claude]

⚠️ Draft — please ignore until reviewed by @ChrisRackauckas.

What changed and why

src/butterflylu.jl calls mul! in 🦋solve! and materializeUV but only imports Diagonal and I from LinearAlgebra, so any use of the butterfly path (🦋workspace / 🦋solve!) throws UndefVarError: mul! not defined in RecursiveFactorization — including the 🦋 testset at test/runtests.jl:80 on current master. This adds mul! to the existing using LinearAlgebra: line. Introduced by 0e635a2 ("refactor butterfly into new struct", PR #103), which dropped the file's plain using LinearAlgebra while keeping bare mul! calls; PR #104 later added two more bare mul! calls in 🦋solve!.

Verification (Julia 1.12.4)

Failing before (unmodified master, bc3bb8a):

$ julia -e 'using Pkg; Pkg.activate(mktempdir()); Pkg.develop(path="<clone>"); using RecursiveFactorization; A=rand(64,64); b=rand(64); RecursiveFactorization.🦋workspace(A,b)'
ERROR: UndefVarError: `mul!` not defined in `RecursiveFactorization`
Suggestion: check for spelling errors or missing imports.
Hint: a global variable of this name also exists in LinearAlgebra.
Stacktrace:
 [1] materializeUV(U::Matrix{Float64}, V::Matrix{Float64}, uv::Vector{Float64})
   @ RecursiveFactorization src/butterflylu.jl:176
 [2] RecursiveFactorization.🦋workspace(A::Matrix{Float64}, b::Vector{Float64}, ::Val{888})
   @ RecursiveFactorization src/butterflylu.jl:40

Passing after (same command plus 🦋solve!, with this one-line fix):

workspace+solve OK

Full test suite (Pkg.test("RecursiveFactorization") on this branch):

Test Summary:         | Pass  Total     Time
Test LU factorization | 3120   3120  2m23.8s
Test Summary: | Pass  Total  Time
🦋            |   21     21  2.1s
     Testing RecursiveFactorization tests passed

Not verified: lts and pre CI lanes (ran locally on 1.12.4 only).

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Root-cause refinement from a parallel investigation: the missing-import was latent since 0e635a2, but the reason CI stayed green until now is that butterflylu.jl's using SparseBandedMatrices re-exported mul! (SBM extends LinearAlgebra.mul!), so the binding resolved transitively. SparseBandedMatrices v1.3.4 — registered today, JuliaRegistries/General#163804 — removed that re-export, which is what surfaced the error ecosystem-wide (it currently aborts LinearSolve's GROUP=Core on master via Core/resolve.jl). SBM 1.3.4 still extends LinearAlgebra.mul!; it just stopped re-exporting the name, so importing it from its owner (LinearAlgebra) as this PR does is the correct durable fix rather than a workaround.